Question: Graph this system of equations and solve. $y = x + 1$ $y = -\dfrac{1}{3} x - 3$ 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 Click and drag the points to move the lines.
Explanation: The y-intercept for the first equation is $1$ , so the first line must pass through the point $(0, 1)$ The slope for the first equation is $1$ . Remember that the slope tells you rise over run. So in this case for every $1$ position you move up You must also move $1$ position to the right. $1$ position to the right. $1$ position up from $(0, 1)$ is $(1, 2)$ Graph the blue line so it passes through $(0, 1)$ and $(1, 2)$ The y-intercept for the second equation is $-3$ , so the second line must pass through the point $(0, -3)$ The slope for the second equation is $-\dfrac{1}{3}$ . Remember that the slope tells you rise over run. So in this case for every $1$ position you move down (because it's negative) You must also move $3$ position to the right. $3$ positions to the right. Graph the green line so it passes through $(0, -3)$ and $(3, -4)$ The solution is the point where the two lines intersect. The lines intersect at $(-3, -2)$.